Are Free Energy Relationships Statistical Artifacts

These arguments do not invalidate the immense array of linear free energy relationships gathered over the past 70 years or so. Class II systems such as Hammett or Taft relationships can be excluded from these considerations because the two variables are independent. The following arguments can be employed to demonstrate experimentally that a Class I correlation such as a Bronsted or a Leffler Equation does not arise from a statistical artifact in a system under investigation. Rearranging the Leffler Equation (Equation 27) yields Equation (29). 

Since the coordinates log/Cf and log/ ,- are independent of each other, a correlation between log/cf and log/ ,- as in Equation (29) would demonstrate the existence of a linear free energy relationship The demonstration of a linear free energy relationship by this means is not necessary for chemical systems because these usually involve substituent change directly adjacent to the reaction centre the correlation is thus chemically reasonable. Application of Equation (29) is significant when the substituent changes may not be so obviously connected with the reaction centre as in the case of the effect of point mutation on conformational changes in enzymes. 

An interesting corollary is that the value of a obtained from Equation (27) is likely to be more accurate than that from Equation (29), because in the former case errors in the two coordinates tend to cancel each other. 

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